HYCO: A formalism for Hybrid-Cooperative PDE modelling

Liverani L, Zuazua Iriondo E (2026)

Publication Language: English

Publication Status: Submitted

Publication Type: Unpublished / Preprint

Future Publication Type: Journal article

Publication year: 2026

Open Access Link: https://dcn.nat.fau.eu/wp-content/uploads/HYCO_Proc_26.02.pdf

Abstract

We present Hybrid-Cooperative Learning (HYCO), a hybrid modeling framework that integrates physics-based and data-driven models through mutual regularization. Unlike traditional approaches that impose physical constraints directly on synthetic models, HYCO treats both components as co-trained agents nudged toward agreement. This cooperative scheme is naturally parallelizable and demonstrates robustness to sparse and noisy data. Numerical experiments on static and time-dependent benchmark problems show that HYCO can recover accurate solutions and model parameters under ill-posed conditions. The framework admits a game-theoretic interpretation as a Nash equilibrium problem, enabling alternating optimization. This paper is based on the extended preprint [6].

Authors with CRIS profile

Lorenzo Liverani Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur) Enrique Zuazua Iriondo Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

How to cite

APA:

Liverani, L., & Zuazua Iriondo, E. (2026). HYCO: A formalism for Hybrid-Cooperative PDE modelling. (Unpublished, Submitted).

MLA:

Liverani, Lorenzo, and Enrique Zuazua Iriondo. HYCO: A formalism for Hybrid-Cooperative PDE modelling. Unpublished, Submitted. 2026.

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